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MiS Preprint

A sparse ${\cal H}$-Matrix Arithmetic, Part II: Application to Multi-Dimensional Problems

Wolfgang Hackbusch and Boris N. Khoromskij


The preceding Part I of this paper has introduced a class of matrices (${\cal H}$-matrices) which are data-sparse and allow an approximate matrix arithmetic of almost linear complexity. The matrices discussed in Part I are able to approximate discrete integral operators in the case of one spatial dimension.
In the present Part II, the construction of ${\cal H}$-matrices is explained for FEM and BEM applications in two and three spatial dimensions. The orders of complexity of the various matrix operations are exactly the same as in Part I. In particular, it is shown that the applicability of ${\cal H}$-matrices does not require a regular mesh. We discuss quasi-uniform unstructured meshes and the case of composed surfaces as well.

MSC Codes:
65F05, 65F30, 65F50
fast algorithms, hierarchical matrices, hierarchical block partioning, sparse matrices, matrix inversion, bem, fem

Related publications

2000 Repository Open Access
Wolfgang Hackbusch and Boris N. Khoromskij

A sparse \( \mathscr{H}\)-matrix arithmetic. Part II. Application to multi-dimensional problems

In: Computing, 64 (2000) 1, pp. 21-47